1. 1 Material Electromagnetic Property Material partition under electric field Material partition under magnetic field Lorentzian model Artificial material

2. 2 Material Partition under Electric Field Dielectrics Conductors

3. 3 Different Dielectrics (Microscopic) non-polarized dielectrics – well described by the Lorentzian model (Microscopic) polarized dielectrics – still not polarized macroscopically due to the random orientation of polarization in microscope, usually described by Clausius- Mossotti’s equation, i.e., Curie’s law modified by the dielectric empty cavity Ferroelectric dielectrics – polarized in macroscope (e.g., BaTiO 3 )

4. 4 Different Dielectrics The permittivity tensor can be diagonalized under proper coordinates transform: Anisotropic dielectrics:

5. 5 Why anisotropic? Highly symmetric dipole distribution in dielectrics generates highly symmetric Coulomb’s potential, which makes the dielectrics more isotropic, and vice versa Equal permittivity along all three axes – isotropic crystal Two of the three permittivities are equal, the 3rd is different – uniaxial crystal (normally refractive index < abnormally refractive index, positive uniaxial, otherwise, negative uniaxial) All three permittivities are different – biaxial crystal

6. 6 Crystal Classification Isotropic – with cubic lattice, e.g., diamond Positive (negative) uniaxial – with trigonal, tetragonal, or hexagonal lattice, e.g., quartz, zircon, rutile, ice (beryl, calcite, tourmaline, sodium nitride) Biaxial – with triclinic, monoclinic, or orthorhombic lattice, e.g., feldspar, mica, topaz, gypsum

7. 7 Crystal Classification Zircon QuartzRutile BerylCalciteTourmaline Feldspar Mica Topaz

8. 8 Material Partition under Magnetic Field If the electron’s orbit has the full symmetry (s-orbit), the microscopic current ring has no specific orientation, the unit inherent magnetic moment (torque) is zero; under the external magnetic field, the inherent symmetry of the unit is broken and an induced magnetic moment appears, with its orientation against the external field; materials made of such units form the diamagnetics If the electron’s orbit is asymmetric, the microscopic current has a specific orientation, the unit has an inherent magnetic moment (the macroscopic magnetic moment is still zero due to the random orientation from unit to unit); under the external magnetic field, the unit magnetic moment will be aligned in the direction of the external field; materials made of such units are the paramagnetics Some materials have aligned magnetic moment units in a small domain, with random alignment only from domain to domain, under even weak external magnetic field, all magnetic moment in different domains can get aligned with (if the unit magnetic moment in a single domain are all aligned), or against (if the unit magnetic moments are contra-aligned in pairs in a single domain) the external field; materials made of such domains are the ferromagnetics (antiferromagnetics)

9. 9 Diamagnetics Origin of diamagnetics: the unit (atom) has no inherent magnetic moment, once is placed in an external magnetic field, extra current is induced in the unit; the induced current must take the opposite direction against the external field, hence the unit induced magnetic moment is in the opposite direction of the external field e r B Finally:

10. 10 Paramagnetics Origin of paramagnetics: the unit (atom) has a built-in magnetic moment, once is place in an external magnetic field, the unit takes the processional motion following the external field B Curie’s law from classical statistical physics The correct form (g - Lande’s factor, j - spin quanta of the unit (atom): Finally:

11. 11 Lorentzian Model The material is viewed as a group of spring bonded flexible electrons on fixed ion centers The motion of a single electron: The (dipole) polarization: The displacement:

12. 12 Lorentzian Model Permittivity for insulators and semiconductors 1 Normal Abnormal For frequency far away from the real part decays more slowly than the imaginary part – that’s why we often take a real dielectric constant with the lossy part ignored.

13. 13 Lorentzian Model Permittivity for metals – the Drude model 1 Normal Abnormal If the loss is negligible, we find The refractive index becomes imaginary. Therefore, inside metals, there is no EM wave can possibly be traveling – only exponentially decayed (i.e., evanescent) wave is allowed.

14. 14 General Electromagnetic Property 0 Dielectrics: Normal EM wave propagation Conductors or plasms: No EM wave direct propagation, EM wave and electron resonance can happen, which support the resonance propagation Ferromagnetics or antiferromagnetics: No EM wave direct propagation, in weak diamagnetics such as gyromagnetics, EM can propagate with attenuation, no reciprocity (chirality) Undiscovered in nature, can be artificially synthesized – Meta materials: EM wave can propagate, with energy and phase moving along opposite direction

15. 15 Meta-material for Microwave

16. 16 Home Work 3 1. Consider the radiation attenuation due to the electron acceleration in Lorentzian model, find the necessary modification to the general formula for material permittivity. 2. *A glass of water contains uniformly distributed small particles made of the same material in scattered size ranging in the neighborhood of microns. In the visible light range, the relative permittivity of the water is around 1.77 from 2000nm to 100nm, whereas the relative permittivity of the particle material is 1.689 at 2000nm and 1.789 at 100nm. What will happen if we shine the glass of water with a beam of the natural light? Think of an application by employing this effect. 3. *Calculate the relative permittivity and permeability of a 3D microwave meta- material built with normal PCB boards (with the structure shown in the previous slide) for Q-band (with wavelength range from 6mm to 9mm). Select one of problem 2 or problem 3 to work with, work out both problems for 5 bonus points.